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What is the Least Common Multiple of 5405 and 5414?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least common multiple (LCM) of 5405 and 5414 is 29262670.

LCM(5405,5414) = 29262670

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Least Common Multiple of 5405 and 5414 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 5405 and 5414, than apply into the LCM equation.

GCF(5405,5414) = 1
LCM(5405,5414) = ( 5405 × 5414) / 1
LCM(5405,5414) = 29262670 / 1
LCM(5405,5414) = 29262670

Least Common Multiple (LCM) of 5405 and 5414 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 5405 and 5414. First we will calculate the prime factors of 5405 and 5414.

Prime Factorization of 5405

Prime factors of 5405 are 5, 23, 47. Prime factorization of 5405 in exponential form is:

5405 = 51 × 231 × 471

Prime Factorization of 5414

Prime factors of 5414 are 2, 2707. Prime factorization of 5414 in exponential form is:

5414 = 21 × 27071

Now multiplying the highest exponent prime factors to calculate the LCM of 5405 and 5414.

LCM(5405,5414) = 51 × 231 × 471 × 21 × 27071
LCM(5405,5414) = 29262670